{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<small><i>This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com). Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_tutorial/).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dimensionality Reduction: Principal Component Analysis in-depth\n",
    "\n",
    "Here we'll explore **Principal Component Analysis**, which is an extremely useful linear dimensionality reduction technique.\n",
    "\n",
    "We'll start with our standard set of initial imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducing Principal Component Analysis\n",
    "\n",
    "Principal Component Analysis is a very powerful unsupervised method for *dimensionality reduction* in data.  It's easiest to visualize by looking at a two-dimensional dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cFz0Uu7ABMBPhjLzINK481F232cwQd+52j2Xsknd78IYkXVpTqd8/cmPBdmED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\nAAAMQzgDAGAYwhkAAMMQzgAAGOb/Axl5mbDvVNp0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "X = np.dot(np.random.random(size=(2, 2)), np.random.normal(size=(2, 200))).T\n",
    "plt.plot(X[:, 0], X[:, 1], 'o')\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that there is a definite trend in the data. What PCA seeks to do is to find the **Principal Axes** in the data, and explain how important those axes are in describing the data distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.7625315  0.0184779]\n",
      "[[-0.94446029 -0.32862557]\n",
      " [-0.32862557  0.94446029]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)\n",
    "print(pca.explained_variance_)\n",
    "print(pca.components_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see what these numbers mean, let's view them as vectors plotted on top of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UkAFFQbldTHheDSQfIJVs5HWq9xIVi5zD2e12w26/9otJr9cjGAzCYDDA7XbD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\n/x/9f85Wxu79nQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[:, 0], X[:, 1], 'o', alpha=0.5)\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    plt.plot([0, v[0]], [0, v[1]], '-k', lw=3)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that one vector is longer than the other. In a sense, this tells us that that direction in the data is somehow more \"important\" than the other direction.\n",
    "The explained variance quantifies this measure of \"importance\" in direction.\n",
    "\n",
    "Another way to think of it is that the second principal component could be **completely ignored** without much loss of information! Let's see what our data look like if we only keep 95% of the variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 2)\n",
      "(200, 1)\n"
     ]
    }
   ],
   "source": [
    "clf = PCA(0.95) # keep 95% of variance\n",
    "X_trans = clf.fit_transform(X)\n",
    "print(X.shape)\n",
    "print(X_trans.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By specifying that we want to throw away 5% of the variance, the data is now compressed by a factor of 50%! Let's see what the data look like after this compression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6ZsaGkxkdpiBiIp4qel5fZ2jeAZ3M6Hjk58DuOyP43asKMmkBluW0hPXKpyyWiURsKArQ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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = clf.inverse_transform(X_trans)\n",
    "plt.plot(X[:, 0], X[:, 1], 'o', alpha=0.2)\n",
    "plt.plot(X_new[:, 0], X_new[:, 1], 'ob', alpha=0.8)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The light points are the original data, while the dark points are the projected version.  We see that after truncating 5% of the variance of this dataset and then reprojecting it, the \"most important\" features of the data are maintained, and we've compressed the data by 50%!\n",
    "\n",
    "This is the sense in which \"dimensionality reduction\" works: if you can approximate a data set in a lower dimension, you can often have an easier time visualizing it or fitting complicated models to the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Application of PCA to Digits\n",
    "\n",
    "The dimensionality reduction might seem a bit abstract in two dimensions, but the projection and dimensionality reduction can be extremely useful when visualizing high-dimensional data.  Let's take a quick look at the application of PCA to the digits data we looked at before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "X = digits.data\n",
    "y = digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797, 2)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(2)  # project from 64 to 2 dimensions\n",
    "Xproj = pca.fit_transform(X)\n",
    "print(X.shape)\n",
    "print(Xproj.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TkzQ2LsFms2GxWIlGI0xPT5FIZJM2p1IpLBYLup5dqqyurmFqapJoNEokEsFu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GQhLlkO6qybOjuwl3dgiFh7hgE505x151mrTi4mkeLaFw5mCW7Y+0abgRmtIma3XRlFEGP/sE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7TnxnJnzyU36uIWrNUB+avpjUP0uMJNBb2/+7u/48iRI7zvfe/j/Pnz/P7v/z6f/vSn+ZM/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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(Xproj[:, 0], Xproj[:, 1], c=y, edgecolor='none', alpha=0.5,\n",
    "            cmap=plt.cm.get_cmap('nipy_spectral', 10))\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives us an idea of the relationship between the digits. Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the digits, **without reference** to the labels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What do the Components Mean?\n",
    "\n",
    "PCA is a very useful dimensionality reduction algorithm, because it has a very intuitive interpretation via *eigenvectors*.\n",
    "The input data is represented as a vector: in the case of the digits, our data is\n",
    "\n",
    "$$\n",
    "x = [x_1, x_2, x_3 \\cdots]\n",
    "$$\n",
    "\n",
    "but what this really means is\n",
    "\n",
    "$$\n",
    "image(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots\n",
    "$$\n",
    "\n",
    "If we reduce the dimensionality in the pixel space to (say) 6, we recover only a partial image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KQq+yslK9evVqcoxEHo3HSOTReIxEHo3HSOTReIxEHo3HSOQBeELjjoAkJycrPz9fCQkJ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\n",
      "text/plain": [
       "<Figure size 950.4x172.8 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from fig_code.figures import plot_image_components\n",
    "\n",
    "with plt.style.context('seaborn-white'):\n",
    "    plot_image_components(digits.data[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But the pixel-wise representation is not the only choice. We can also use other *basis functions*, and write something like\n",
    "\n",
    "$$\n",
    "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n",
    "$$\n",
    "\n",
    "What PCA does is to choose optimal **basis functions** so that only a few are needed to get a reasonable approximation.\n",
    "The low-dimensional representation of our data is the coefficients of this series, and the approximate reconstruction is the result of the sum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "911646d08f3349f388d0a76fd28085aa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from fig_code.figures import plot_pca_interactive\n",
    "plot_pca_interactive(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that with only six PCA components, we recover a reasonable approximation of the input!\n",
    "\n",
    "Thus we see that PCA can be viewed from two angles. It can be viewed as **dimensionality reduction**, or it can be viewed as a form of **lossy data compression** where the loss favors noise. In this way, PCA can be used as a **filtering** process as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing the Number of Components\n",
    "\n",
    "But how much information have we thrown away?  We can figure this out by looking at the **explained variance** as a function of the components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nDgBg/PjxjcK9NTOZLThyqgj+vgr07xbu6nKIiMgD2Q3vkpISbN68GWvWrMHY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\nD/P/uTmzY6JHLM4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA().fit(X)\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that our two-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance.  Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in multiple observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA as data compression\n",
    "\n",
    "As we mentioned, PCA can be used for is a sort of data compression. Using a small ``n_components`` allows you to represent a high dimensional point as a sum of just a few principal vectors.\n",
    "\n",
    "Here's what a single digit looks like as you change the number of components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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W4t2DHuWpcJaQeLe1VlhjksUk/fHIXvSb5bOKpdYSfTP76o//ObHqk9L94vsYd2AcPh/0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\nYII=\n",
      "text/plain": [
       "<Figure size 576x576 with 64 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(8, 8, figsize=(8, 8))\n",
    "fig.subplots_adjust(hspace=0.1, wspace=0.1)\n",
    "\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    pca = PCA(i + 1).fit(X)\n",
    "    im = pca.inverse_transform(pca.transform(X[20:21]))\n",
    "\n",
    "    ax.imshow(im.reshape((8, 8)), cmap='binary')\n",
    "    ax.text(0.95, 0.05, 'n = {0}'.format(i + 1), ha='right',\n",
    "            transform=ax.transAxes, color='green')\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take another look at this by using IPython's ``interact`` functionality to view the reconstruction of several images at once:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4d8ec80b3f19489195eb067643ea03c0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "def plot_digits(n_components):\n",
    "    fig = plt.figure(figsize=(8, 8))\n",
    "    plt.subplot(1, 1, 1, frameon=False, xticks=[], yticks=[])\n",
    "    nside = 10\n",
    "    \n",
    "    pca = PCA(n_components).fit(X)\n",
    "    Xproj = pca.inverse_transform(pca.transform(X[:nside ** 2]))\n",
    "    Xproj = np.reshape(Xproj, (nside, nside, 8, 8))\n",
    "    total_var = pca.explained_variance_ratio_.sum()\n",
    "    \n",
    "    im = np.vstack([np.hstack([Xproj[i, j] for j in range(nside)])\n",
    "                    for i in range(nside)])\n",
    "    plt.imshow(im)\n",
    "    plt.grid(False)\n",
    "    plt.title(\"n = {0}, variance = {1:.2f}\".format(n_components, total_var),\n",
    "                 size=18)\n",
    "    plt.clim(0, 16)\n",
    "    \n",
    "interact(plot_digits, n_components=[1, 64], nside=[1, 8]);"
   ]
  },
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   "source": [
    "## Other Dimensionality Reducting Routines\n",
    "\n",
    "Note that scikit-learn contains many other unsupervised dimensionality reduction routines: some you might wish to try are\n",
    "Other dimensionality reduction techniques which are useful to know about:\n",
    "\n",
    "- [sklearn.decomposition.PCA](http://scikit-learn.org/0.13/modules/generated/sklearn.decomposition.PCA.html): \n",
    "   Principal Component Analysis\n",
    "- [sklearn.decomposition.RandomizedPCA](http://scikit-learn.org/0.13/modules/generated/sklearn.decomposition.RandomizedPCA.html):\n",
    "   extremely fast approximate PCA implementation based on a randomized algorithm\n",
    "- [sklearn.decomposition.SparsePCA](http://scikit-learn.org/0.13/modules/generated/sklearn.decomposition.SparsePCA.html):\n",
    "   PCA variant including L1 penalty for sparsity\n",
    "- [sklearn.decomposition.FastICA](http://scikit-learn.org/0.13/modules/generated/sklearn.decomposition.FastICA.html):\n",
    "   Independent Component Analysis\n",
    "- [sklearn.decomposition.NMF](http://scikit-learn.org/0.13/modules/generated/sklearn.decomposition.NMF.html):\n",
    "   non-negative matrix factorization\n",
    "- [sklearn.manifold.LocallyLinearEmbedding](http://scikit-learn.org/0.13/modules/generated/sklearn.manifold.LocallyLinearEmbedding.html):\n",
    "   nonlinear manifold learning technique based on local neighborhood geometry\n",
    "- [sklearn.manifold.IsoMap](http://scikit-learn.org/0.13/modules/generated/sklearn.manifold.Isomap.html):\n",
    "   nonlinear manifold learning technique based on a sparse graph algorithm\n",
    "   \n",
    "Each of these has its own strengths & weaknesses, and areas of application. You can read about them on the [scikit-learn website](http://sklearn.org)."
   ]
  }
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